Finite Group Databasebeta

← #11794338

Subgroups — #11794338

Order 1152.

549 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63650C211yesmaximal, characteristic
2C2×C3×#822C211yesmaximal, characteristic, complemented
3C3×#5121C211yesmaximal, characteristic, complemented
4#10591116C211yesmaximal, characteristic, complemented
5#10591096C211yesmaximal, characteristic
6C2×#63564C211yesmaximal, characteristic
7#10589167C211yesmaximal, characteristic, complemented
8#70715—31nomaximal
9#70676—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63650—22no—
18C3×#822—22no—
19C3×#818—21no—
20C3×#817—21no—
21Dic3⋊(C3⋊C8)—22no—
22#63564—21no—
23#63564—21no—
24#63564—22no—
25C2×C3×#108—31no—
26C3×#428—31no—
27#5131—31no—
28C2×#823—31no—
29C2×#823—31no—
30C2×#823—61no—
31C2×#822D311yescharacteristic, complemented
32#5121D311yescharacteristic, complemented
33C2×#821—31no—
34#5102—31no—
35#5001—31no—
36#4999—31no—
37C2×#809—31no—
38#4554—31no—
39#4530—31no—
40C23×C3⋊D3—21no—
41C22×C32×C4C2311yescharacteristic
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)Q812yes—
48C22×C3×Dic3—21no—
49C32×M16—21no—
50C32×M16D412yes—
51C2×C32×C8—21no—
52#3748—21no—
53#3748—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×#217—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4×Dic3—21no—
61C3×#208—21no—
62C3×#208—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8D412yes—
67#2063—91noSylow
68C22×D12—31no—
69C22×D12—31no—
70C22×D12—61no—
71C2×C3×M16—21no—
72C2×C3×M16—31no—
73C2×C3×M16C2×D311yescharacteristic
74C2×C3×M16C2×D311yescharacteristic
75C22×C3×C8—31no—
76C3×#117—31no—
77C2×C3×C4⋊C4—31no—
78#926C2×D311yescharacteristic
79C2×C4⋊Dic3C2×D311yescharacteristic
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—61no—
83C2×#208C2×D311yescharacteristic
84C22×C3⋊C8C2×D311yescharacteristic
85C3×#108—62no—
86C3×#107—61no—
87C3×#106—61no—
88#823—64no—
89#823—62no—
90#823—62no—
91#822—22no—
92#821—62no—
93#821—61no—
94#821—61no—
95#818—21no—
96#817—21no—
97Dic3⋊C8—62no—
98#809—61no—
99#809—61no—
100#809—62no—
101C4⋊(C3⋊C8)—62no—
102C23×C32#4111yescharacteristic
103C22×C3⋊D3—22no—
104C22×C3⋊D3—41no—
105C22×C3⋊D3—41no—
106C22×C3⋊D3—81no—
107C22×C3⋊D3—81no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×Q811yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C4⋊(C3⋊D3)—22no—
115C4⋊(C3⋊D3)—22no—
116C4⋊(C3⋊D3)—41no—
117C4⋊(C3⋊D3)—41no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—41no—
121C2×C3×Dic3—81no—
122C32×C8—22no—
123C3⋊(C3⋊C8)—41no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—41no—
126C2×#108—31no—
127#428—31no—
128#424—91no—
129#418—91no—
130C2×#102—91no—
131C2×#100—91no—
132#343—91no—
133C23×D3—62no—
134C23×D3—61no—
135C23×D3—61no—
136C22×C3×C4—21no—
137C22×C3×C4—61no—
138C22×C3×C4C22×D311yescharacteristic
139C22×C3×C4C22×D311yescharacteristic
140C22×Dic3—21no—
141C2×D12—32no—
142C2×D12—32no—
143C2×D12—62no—
144C2×D12—61no—
145C2×D12—61no—
146C2×D12—61no—
147C2×D12—61no—
148C2×D12—61no—
149C2×D12—61no—
150C2×D12—61no—
151C2×D12—61no—
152C2×D12—62no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—121no—
156C2×D12—121no—
157C2×D12—121no—
158C2×D12—121no—
159C3×M16—21no—
160C3×M16—21no—
161C3×M16—22no—
162C3×M16—41no—
163C3×M16—61no—
164C3×M16—61no—
165C3×M16D1212yes—
166C3×M16#6712yes—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—32no—
170C2×C3×C8—41no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C3×C4⋊C4—31no—
175C3×C4⋊C4—31no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C22⋊C4—61no—
179C3×C42—61no—
180#217—21no—
181C4⋊Dic3—21no—
182C4⋊Dic3—21no—
183C4⋊Dic3#6711yescharacteristic
184C4⋊Dic3#6711yescharacteristic
185C4×Dic3—21no—
186#208—21no—
187#208—21no—
188#208—62no—
189#208—61no—
190#208—61no—
191#208—61no—
192#208—61no—
193#208—121no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—61no—
199C2×C3⋊C8—121no—
200C2×C3⋊C8D1212yes—
201C22×C32—21no—
202C22×C32—21no—
203C22×C32#12111yescharacteristic
204C22×C32C22⋊Q811yescharacteristic
205C22×C32#12611yescharacteristic
206C2×C3⋊D3—42no—
207C2×C3⋊D3—82no—
208C2×C3⋊D3—81no—
209C2×C3⋊D3—81no—
210C2×C3⋊D3—82no—
211C32×C4#12111yescharacteristic
212C32×C4#12111yescharacteristic
213C32×C4C22⋊Q811yescharacteristic
214C32×C4C22⋊Q811yescharacteristic
215C3×Dic3—41no—
216C3×Dic3—41no—
217C3×Dic3—81no—
218C22×D4—91no—
219C2×M16—31no—
220C2×M16—91no—
221C2×M16D3211yescharacteristic
222C22×C8—31no—
223#117—31no—
224C2×C4⋊C4—31no—
225#108—62no—
226#107—61no—
227#106—61no—
228C4⋊C8—182no—
229#102—181no—
230#102—181no—
231#102—182no—
232#100—182no—
233C23×C3—21no—
234C23×C3#23711yescharacteristic
235C23×C3#23911yescharacteristic
236C22×D3—64no—
237C22×D3—62no—
238C22×D3—62no—
239C22×D3—122no—
240C22×D3—122no—
241C22×D3—121no—
242C22×D3—121no—
243C22×D3—121no—
244C22×D3—121no—
245C22×D3—241no—
246C22×D3—241no—
247C22×D3—241no—
248C22×D3—241no—
249C22×D3—242no—
250C22×D3—242no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—121no—
260C2×C3×C4—241no—
261C2×C3×C4C2×D1211yescharacteristic
262C2×C3×C4C2×D1211yescharacteristic
263C2×C3×C4#23511yescharacteristic
264C2×C3×C4#23511yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4#23711yescharacteristic
268C2×C3×C4D3×Q811yescharacteristic
269C2×C3×C4D3×Q811yescharacteristic
270C2×C3×C4#23911yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273C2×Dic3—21no—
274C2×Dic3—21no—
275C2×Dic3—41no—
276C2×Dic3—81no—
277D12—62no—
278D12—62no—
279D12—62no—
280D12—62no—
281D12—122no—
282D12—122no—
283D12—122no—
284D12—122no—
285D12—121no—
286D12—121no—
287D12—121no—
288D12—121no—
289C3×C8—22no—
290C3×C8—22no—
291C3×C8—42no—
292C3×C8—62no—
293C3×C8—121no—
294C3⋊C8—22no—
295C3⋊C8—41no—
296C3⋊C8—122no—
297C3⋊C8—121no—
298C3⋊C8—121no—
299C2×C32—21no—
300C2×C32—21no—
301C2×C32#39611yescharacteristic
302C2×C32#47111yescharacteristic
303C2×C32#47211yescharacteristic
304C3⋊D3—82no—
305C24—181no—
306C2×D4—92no—
307C2×D4—181no—
308C2×D4—181no—
309C2×D4—181no—
310C2×D4—181no—
311C2×D4—181no—
312C22×C4—61no—
313C22×C4C2×D3211yescharacteristic
314M16—21no—
315M16—61no—
316M16—61no—
317M16—181no—
318M16—181no—
319M16#62612yes—
320C2×C8—21no—
321C2×C8—32no—
322C2×C8—61no—
323C2×C8—61no—
324C2×C8—61no—
325C2×C8—181no—
326C4⋊C4—31no—
327C4⋊C4—31no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C22⋊C4—61no—
331C42—61no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3#89511yescharacteristic
342C22×C3#89711yescharacteristic
343C22×C3#89811yescharacteristic
344C22×C3#89811yescharacteristic
345C22×C3#93911yescharacteristic
346C22×C3#94611yescharacteristic
347C2×D3—124no—
348C2×D3—122no—
349C2×D3—122no—
350C2×D3—242no—
351C2×D3—242no—
352C2×D3—242no—
353C2×D3—242no—
354C2×D3—244no—
355C2×D3—241no—
356C2×D3—241no—
357C2×D3—241no—
358C2×D3—241no—
359C2×D3—242no—
360C2×D3—242no—
361C2×D3—244no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—121no—
367C3×C4—121no—
368C3×C4—241no—
369C3×C4#89511yescharacteristic
370C3×C4#89611yescharacteristic
371C3×C4#89611yescharacteristic
372C3×C4#89711yescharacteristic
373C3×C4#93011yescharacteristic
374C3×C4#93011yescharacteristic
375C3×C4#93911yescharacteristic
376C3×C4#94611yescharacteristic
377Dic3—41no—
378Dic3—41no—
379Dic3—81no—
380C32#206311yescharacteristic, complemented, Sylow
381C23—182no—
382C23—361no—
383C23—361no—
384C23—721no—
385C23—721no—
386C23#379611yescharacteristic
387D4—182no—
388D4—182no—
389D4—361no—
390D4—361no—
391C2×C4—61no—
392C2×C4—61no—
393C2×C4—121no—
394C2×C4—241no—
395C2×C4#379711yescharacteristic
396C2×C4#379911yescharacteristic
397C2×C4D3×D1211yescharacteristic
398C2×C4#380411yescharacteristic
399C2×C4C2×#62611yescharacteristic
400C2×C4D3×#6711yescharacteristic
401C8—22no—
402C8—62no—
403C8—121no—
404C8—361no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—41no—
413C2×C3—41no—
414C2×C3#489711yescharacteristic
415C2×C3#489811yescharacteristic
416C2×C3#499411yescharacteristic
417C2×C3#499411yescharacteristic
418C2×C3#519911yescharacteristic
419C2×C3#520311yescharacteristic
420D3—244no—
421D3—242no—
422D3—242no—
423C22—21no—
424C22—21no—
425C22—362no—
426C22—722no—
427C22—722no—
428C22—721no—
429C22—721no—
430C22#6384811yescharacteristic
431C22#6387111yescharacteristic
432C22#6388611yescharacteristic
433C4—121no—
434C4—121no—
435C4—241no—
436C4#6388811yescharacteristic
437C4#6389511yescharacteristic
438C4#6390911yescharacteristic
439C4#6397811yescharacteristic
440C3—21no—
441C3#7067611yescharacteristic, complemented
442C3#7071511yescharacteristic, complemented
443C2—21no—
444C2—21no—
445C2—722no—
446C2#1059098411yescharacteristic
447C2#1059098511yescharacteristic
448C2#1059131111yescharacteristic
subgroupG/H
centerC22#63886
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×M16D32
hypocenterC32#2063
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C3×#822C2semidirect
3. C3×#5121C2semidirect
4. #10591116C2semidirect
7. #10589167C2semidirect
31. C2×#822D3semidirect
32. #5121D3semidirect
380. C32#2063semidirect
441. C3#70676semidirect
442. C3#70715semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#636502
C2×C3×#8222
C3×#51212
#105911162
#105910962
C2×#635642
#105891672
#707153
#706763